$A$ proton of mass $m$ and charge $+e$ is moving in a circular orbit in a magnetic field with energy $1\, MeV$. What should be the energy of $\alpha$-particle (mass = $4m$ and charge = $+2e$) so that it can revolve in the path of the same radius?

$A$ particle of specific charge $q / m = \pi \text{ C kg}^{-1}$ is projected from the origin towards the positive $X$-axis with a velocity $10 \text{ ms}^{-1}$ in a uniform magnetic field $\vec{B} = -2 \hat{k} \text{ T}$. The velocity $\vec{v}$ of the particle after time $t = \frac{1}{12} \text{ s}$ will be (in $\text{ ms}^{-1}$):

$A$ charge '$q$' moves with a velocity $2 \ m/s$ along the $x$-axis in a uniform magnetic field $\vec{B} = (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) \ T$. The charge will experience a force:

An electron is projected with uniform velocity along the axis of a current-carrying long solenoid. Which of the following is true?

In a Bainbridge mass spectrograph,a potential difference of $1000 \ V$ is applied between two plates separated by a distance of $1 \ cm$. If the magnetic field is $B = 1 \ T$,what is the velocity of the undeflected positive ions in $m/s$ from the velocity selector?

$A$ particle of charge $q$,mass $m$ and kinetic energy $E$ enters a magnetic field perpendicular to its velocity and undergoes a circular arc of radius $r$. Which of the following curves represents the variation of $r$ with $E$?